Algebraische Flächen visualisieren mit SURFER

In diesem Artikel geht es um das Programm SURFER, welches es ermöglicht algebraische Flächen zu visualisieren.

#Math #Mathematik #Bildgenerator #Algebra #SURFER #Unterrichtsmaterialien #Schule #Hochschule #Universität #Linux

https://gnulinux.ch/surfer

Don’t ask me why, but I came up with an ‘adversarial graph coloring game’, where players each color a vertex per turn, and the first player who is forced to color a vertex connected to a vertex they already coloured loses.

Is this game and its complexity known?

#maths #math #mathgames

💁🏻‍♀️ TIL: 🦊🔢 Archaeologists have identified #Saktahnwaax, a #Maya mathematician-astronomer from around 800 CE, as the first named scientist of the pre-Columbian Americas.

Found in a painted chamber at #Xultun, #Guatemala, his name appears alongside advanced formulas, including a 2,920 day cycle that integrates #solar and #Venus years.

👉 https://zurl.co/71Jy0

#archaeology #astronomy #math #ancient #science #precolumbian #mesoamerica #indigenous #history #art

Last year, I took a class on Chaos and Fractals at UVM. I thought it'd just be a fun way to get a math credit, but it ended up having a profound impact on how I see the world. My latest blog post is all about chaos, and the new perspective it gave me. What is randomness, anyway? Why does nature sometimes repeat itself, but not exactly? And how do living things interact with the complexity?

https://thinkingwithnate.wordpress.com/2026/07/01/chaos/
#math #chaos #complexity

Hungry? Have a bowl of ramenujan.

Thirsty? Have a cup of lissajuice.

Feeling sick? Drink some mandelbroth.

#math #shitpost

Aggadah Haggadah - WORLD WITHOUT END

The concept of multiple YOU and multiple EXISTENCE is not new, conceptually speaking and exists both abstractly and concretely.

#math #history #dream #errtling #paranormal-things #cosmology #philosophy #bookcafe #celtic #past-lives

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Aggadah Haggadah - WORLD WITHOUT END The concept of multiple YOU and multiple EXISTENCE is not new, conceptually speaking and exists both abstractly and concretely. #math #history #dream #errtling #paranormal-things #cosmology #philosophy #bookcafe #celtic #past-lives

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Aggadah Haggadah - WORLD WITHOUT END The concept of multiple YOU and multiple EXISTENCE is not new, conceptually speaking and exists both abstractly and concretely. #math #history #dream #errtling #paranormal-things #cosmology #philosophy #bookcafe #celtic #past-lives

Reminder: if you're a secondary-school teacher, and want to give your students a hands-on activity for learning logarithms, my site

https://cardboard-computer.org/

is free (libre and gratuit) and has no ads, analytics, or tracking cookies. You can download templates to build your own sliderule, and there are instructions and interactive exercises for using it.

(Tell them it's a steampunk calculator.)

#slideRules #teaching #math

mandelbrot 10:06

md formatted

syntax

• nice -19 fraqtive &
• type julia
• variant absolute Im.
• parameters x 0.62 y 0.5
• exponent real=2.91
• formula Z(n+1)=(ReZ(n)+I|Im(Zn)|)2.91+C
• zoom 10

  -0.35

• rotation 46.0 deg
• generation 2D
• Resolution Width 2560 Height 1080
• Anti Aliasing Medium
• Multisampling 4x4
• Calculation time a few s

Julia Mandelbrot

sources:

man fraqtive(1)

man thunar(1)

Advanced fractal mathematics by Gerold van Dijk

https://en.wikipedia.org/wiki/Mathematics

https://en.wikipedia.org/wiki/Mandelbrot_set

https://en.wikipedia.org/wiki/Mandelbrot_set#Relationship_with_Julia_sets

https://en.wikipedia.org/wiki/Hausdorff_dimension

https://en.wikipedia.org/wiki/File:Self-Similarity-Zoom.gif

#mathematics #math #coprocessor #programming #mandelbrot #fractals #advanced #Lineair #Algebra #complex #numbers #formulas #matrix #technology #OpenSource #no #TV#

@amiga

Mathstodon.xyz is a Mastodon server for people who love maths. We have LaTeX rendering in the web interface! We hope there’ll be lots of maths chat, but any topic of conversation following the code of conduct and the principle of getting along together is OK.

This server has a post size of up to 1729 characters.

https://mathstodon.xyz

You can find out more at https://mathstodon.xyz/about or contact the admin account @christianp

#FeaturedServer #Mathematics #Maths #Math #Mastodon

scala> type Something = Nothing => Nothing
// defined alias type Something = Nothing => Nothing
                                                                                                                                                                                    
scala> summon[Something =:= Nothing]
-- [E172] Type Error: ----------------------------------------------------------
1 |summon[Something =:= Nothing]
  |                             ^
  |                             Cannot prove that Something =:= Nothing.
1 error found

1/3
#MathsMonday #Math
I've seen 2 people in #Mathematics claim recently that we can't prove that a+b=b+a - the Commutative Property - and that we just accept it as true. Nope, not only is it literally proven, but we show students the proof when we teach this to them. File this under "Mathematicians forget what they were taught in high school, again" (along with The Distributive Law, which I just happened to be teaching to my Year 7's last week). There are multiple #Maths proofs of this...

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Picture depicting the Commutative Property for Addition and Multiplication

The superposition principle,[1] also known as superposition property, states that, for all linear systems, the net response caused by two or more stimuli is the sum of the responses that would have been caused by each stimulus individually. So that if input A produces response X, and input B produces response Y, then input (A + B) produces response (X + Y).

https://en.wikipedia.org/wiki/Superposition_principle

#physics #math #caturday #caturdayeveryday

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orange and white cat, balanced between two states, as all things should be

The Unexpected Math Behind Van Gogh’s “Starry Night”

If you’ve taken a good art history course on the Impressionists and Post-Impressionists, you...

Archive: ia: https://s.faithcollapsing.com/p6xw7

#art #math
https://www.openculture.com/2026/05/the-math-behind-van-goghs-starry-night.html

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The Unexpected Math Behind Van Gogh’s “Starry Night”

We have updated our #PhET scraper for Free online #physics, #chemistry, #biology, earth #science and #math simulations.

Here is the source code: https://github.com/openzim/phet/releases/tag/v3.1.2

Here is the packaged software: https://www.npmjs.com/package/phetscraper

Here are the ZIM #offline archives: https://browse.library.kiwix.org/#category=phet

#FOSS #edtech

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Screenshots of PhET computer simulations

The #AI solution to #erdos problem 1196 made it onto #bbc More or Less

#maths #mathematics #math

Happy birthday to #mathematician Maryam Mirzakhani (1977-2017)! The Fields Medal, one of the most prestigious #math awards, is awarded to mathematicians < 40. In 2014, she became 1st woman to win. Her research included Teichmüller theory, hyperbolic geometry, ergodic theory, & symplectic geometry, and Fields committee cited her work in “the dynamics and geometry of Riemann surfaces and their moduli spaces”.⁠
⁠🧵1/
⁠
#sciart #mathart #linocut #printmaking #womeninSTEM #histsci

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Linocut portrait on 11”x14” white washi paper of Maryam Mirzakhani in a gradient of deep red at the bottom to dark blue at the top, 3/4 view from the top of her shoulders up. She has short hair, wears a tshirt and looks at the viewer. She is surrounded by mathematical doodles and diagrams in light blue.

#Philosophy/ #physics / #math poll:

Is it fair to describe quantity as having agency? I.e., is quantity as such a causal force?

Sorry to force a binary choice, happy to read comments.

In geometry and trigonometry, a right angle is an angle of exactly 90 degrees or ⁠ π/2⁠ radians[1] corresponding to a quarter turn.[2] If a ray is placed so that its endpoint is on a line and the adjacent angles are equal, then they are right angles.[3] The term is a calque of Latin angulus rectus; here rectus means "upright", referring to the vertical perpendicular to a horizontal base line.

#longcat #void #math #caturday #caturdayeveryday

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right angle void longcat

Time for another round of examining the interesting beliefs of SmartmanApps and #debunking the #disinformation this #MathsMonday.

We saw last time that his view of mathematics is at odds with that of the mainstream: I enumerated the standard axioms of the real numbers and proved that there can be no number 0.999… that is simultaneously less than 1 and greater than 0.9, 0.99, and any such finite decimal truncation of 0.999….

His idea is that 1 is “the limit of” 0.999…, but not the exact value of it. But what exactly is a limit? Let’s have a look at what our Smart Friend calls a limit:

> The limit is the number which [the sequence] never reaches

(see https://dotnet.social/@SmartmanApps/116303201093245275 I am not quite certain he intends this language to apply to all sequences, but I have not seen other descriptions from him)

This is simply inadequate, and it’s worth seeing why such poor explanations are inadequate with some examples.

* The sequence (1, 1, 1, …) *never reaches* the number 2, so is 2 the limit? The same applies for every number greater than 1, so are all of them the limit? The wording “the number” implies that the limit should be unique.
* On the other hand, it *does* reach 1, which intuition says ought to be the limit of this sequence.
* The sequence (1, 2, 3, 4, …) will exceed every number eventually and so, I guess, “reaches” every number. Again the wording “the number” suggests that such a number always exists, but apparently does not.

It may be that the Genius has a more precise idea of limit lurking in his mind, but to tease it out we’d have to interrogate him about these (and probably other) examples, and most likely anyone who tried would get blocked before they could complete their investigation.

The usual definition can be seen clearly from the early 19th century, due to Bolzano, though its roots go back further. That definition is:

> For a sequence (a_0, a_1, a_2, …), and a real number A, if for every real number ε > 0, there is some natural number N such that for every n > N, |a_n - A| < ε, then we say that A is the limit of the sequence (a_0, a_1, a_2, …).

This is quite a mouthful, and first year mathematics undergraduates spend quite some time getting the hang of it. A characteristic of the definition is the alternating *quantifiers*, which are written out “for every” and “there is” here (but would normally be written with symbols). It took mathematicians some time to come up with this modern version of quantified mathematical language.

Nevertheless we can put it into simpler language, at the cost of a little precision: **the limit of a sequence is A if the sequence gets as close to A as we like and remains that close forever**. It’s important that we keep that “remains that close” in. It’s important that neither of these ways of describing the concept assume a limit exists, because not all sequences have a limit. It is quite easy to prove directly from the definition and the properties of the real numbers that:

* A constant sequence (a, a, a, …) has a as its limit
* If a sequence has a limit, the limit is unique
* The sequence (1, 2, 3, …) does not have a limit

The ordinary way of proving such basic facts is via our friends Completeness and the Archimedean property. Our pal has explicitly rejected these (by affirming the existence of infinitesimals) and so does not have them available for this purpose.

To see this practically, how should we prove that the limit of the sequence (0.9, 0.99, 0.999, …) is 1? The ordinary way would be to appeal to the definition:

1. Pick any positive distance ε. By the Archimedean property, ε > 1/N > 1/10^N for some N
2. If n > N then 1-0.99…99 (with n nines) is less than 1/10^N < ε, so 1 is the limit.

The astute reader will notice this argument is very similar to the one from last week. But if infinitesimals exist, we *cannot do this*: the first step is, in fact, false. If ε is infinitesimal, then there will not be any N such that ε > 1/N! That is in fact what it means to be infinitesimal!

Specifically, if ε = 1 - 0.999…, which the Smart Man says is greater than zero, this argument falls down; we cannot get the sequence (0.9, 0.99, 0.999, …) to be ε-close to 1 if ε is infinitesimal by looking to some point far enough into the sequence: for any n, the nth term 1/10^n away from 1, and 1/10^n is larger than ε.

From further reading of SmartmanApps’ posts, I suspect he might want to object that if we continue the sequence “to infinity” the difference becomes infinitesimal. I should be very clear here: sequences as here defined and as used by him cannot be continued “to infinity”. The defining rule for this sequence is that the nth term is 1 - 1/10^n, something which makes sense and is defined for *natural numbers* n, and because infinity is not a natural number and 10^∞ is not defined, we can’t just continue like that. The only way would be to make a *definition* of what 1 - 1/10^∞ means, i.e. to *choose* what happens at this continuation; there are no axioms governing rational numbers that force us to give a certain value to this expression.

Another potential objection is that I have used the “wrong” definition of a limit, but:

1. You can find this definition in every single textbook and set of lecture notes on real analysis
2. You can find this definition (written in an old fashioned way of "variables that take on successive values" rather than sequences) in the 120-year old algebra textbooks he loves to cite
3. We saw multiple problems with his broken pseudo-definition that make it useless

so it’s up to him to provide a correct one. One could try as a first attempt to replace “for every real number greater than zero” with “for every non-infinitesimal real number greater than zero”. But without Completeness, basic facts like the uniqueness of limits, on which many more important theorems rest, would still be false.

It’s fun to explore what happens to mathematics if throw out some of its founding principles, though it does make doing anything useful with it hard. Forget working out anything truly useful like calculus without Completeness, or something precise to replace it!

Next time I plan to look a bit more at infinitesimals and how you can treat them rigorously.

#maths #math #mathematics

I'm counting my calorie intake. With #SelfHosted #SparkyFitness, of course.

Also, my wife is baking a lot, and it is a problem when I need to track that "custom" food somehow. So instead of guessing, I'm now calculating nutrition values of her recipes.

#math #calculation

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A table of recipe ingredients with weight, calories, and nutrition values for each. The bottom rows contain the overall ingredients' weights, calories, and nutritional values, as well as the same values per 100 grams. Ingredient names are written in Ukrainian. Also, there is a title above the table in Ukrainian reading “Marble cookies".

Modern mathematics is full of holes. Mathematicians created definitions that are unrealistic in reality. Too much notation and definitions often hide flaws in their proofs. Here is a simple example.

Is Q dense in R? The proof of Q dense in R has been widely accepted by most if not all #mathematicians. Yet, there is an obvious mistake that was never noticed, namely, Q is not just any countable set. Q is an ordered set. Their proof completely omitted this critical property.

#math #mathematics

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Modern mathematics is full of holes. Mathematicians created definitions that are unrealistic in reality. Too much notation and definitions often hide flaws in their proofs. Here is a simple example. Is Q dense in R? The proof of Q dense in R has been widely accepted by most if not all #mathematicians. Yet, there is an obvious mistake that was never noticed by them, namely, Q is not just any countable set. Q is an ordered set. Their proof omitted this critical property.

Alt...

Modern mathematics is full of holes. Mathematicians created definitions that are unrealistic in reality. Too much notation and definitions often hide flaws in their proofs. Here is a simple example. Is Q dense in R? The proof of Q dense in R has been widely accepted by most if not all #mathematicians. Yet, there is an obvious mistake that was never noticed by them, namely, Q is not just any countable set. Q is an ordered set. Their proof omitted this critical property.

Alt...

Modern mathematics is full of holes. Mathematicians created definitions that are unrealistic in reality. Too much notation and definitions often hide flaws in their proofs. Here is a simple example. Is Q dense in R? The proof of Q dense in R has been widely accepted by most if not all #mathematicians. Yet, there is an obvious mistake that was never noticed by them, namely, Q is not just any countable set. Q is an ordered set. Their proof omitted this critical property.

Alt...

Modern mathematics is full of holes. Mathematicians created definitions that are unrealistic in reality. Too much notation and definitions often hide flaws in their proofs. Here is a simple example. Is Q dense in R? The proof of Q dense in R has been widely accepted by most if not all #mathematicians. Yet, there is an obvious mistake that was never noticed by them, namely, Q is not just any countable set. Q is an ordered set. Their proof omitted this critical property.

1 ball + 1 ball = 2 balls
1 km + 1 km = 2 kms.

1 ball / 2 men = 1/2 ball/men?

1/2 is a rational number. By omitting its unit of measurement, it seems legitimate. In reality, you can't divide a ball between 2 men.

Treating the integer 1 as if it is the same as the real number 1 creates many logical problems in math.

The problem in complex analysis is more serious, when they treat all the + - x / operators as being the same in real and complex number systems.

#math #AI #copilot #deepseek

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Math operators are not defined based on their meanings in reality. Mathematicians do not care about the real meanings of the notations and assumptions in their mathematical systems.

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Math operators are not defined based on their meanings in reality. Mathematicians do not care about the real meanings of the notations and assumptions in their mathematical systems.

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Math operators are not defined based on their meanings in reality. Mathematicians do not care about the real meanings of the notations and assumptions in their mathematical systems.

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Math operators are not defined based on their meanings in reality. Mathematicians do not care about the real meanings of the notations and assumptions in their mathematical systems.

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#MathsMonday #Mathematics
This rubbish article https://www.scientificamerican.com/article/mathematicians-cant-agree-on-whether-0-999-equals-1/ popped up in my feed a few times, and I've already debunked the various points, but will cover it with specific links for each (non-)point.

"Mathematicians can’t agree on whether 0.999... equals 1" - yes they can, it's not, as per division, limits, infinite decimals, and other #Maths topics, all found in #Math textbooks

"by Manon Bischoff" - "is a theoretical Physicist". Maybe just stay in your lane dude... 🙄

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Graph of the hyperbola 1/x, showing that it never reaches 0

I would suggest that folks who think using AI is great for mathematicians should think again. It seems as little as 10 minutes of use can be problematic. What else do we know that provides short-term gains at the expense of long-term loss?

Here, through a series of randomized controlled trials on human-AI interactions (N = 1,222), we provide causal evidence for two key consequences of AI assistance: reduced persistence and impairment of unassisted performance. Across a variety of tasks, including mathematical reasoning and reading comprehension, we find that although AI assistance improves performance in the short-term, people perform significantly worse without AI and are more likely to give up. Notably, these effects emerge after only brief interactions with AI (approximately 10 minutes). These findings are particularly concerning because persistence is foundational to skill acquisition and is one of the strongest predictors of long-term learning.

#AI #GenAI #GenerativeAI #AgenticAI #AIAssistants #CognitiveImpairment #math #MathematicalReasoning #ReadingComprehension

🍕📐 Mathematicians used #geometry to solve the problem of dividing a circular shape into equal areas using off-center slices.

The #research explains how the curvature of a slice affects its structural integrity and its ability to hold toppings.

👉 https://www.scientificamerican.com/article/the-mathematically-correct-way-to-slice-a-pizza/

#math #science #pizza #physics #logic #topology

We knew, but the proof is nice.

"Apple just proved that AI models cannot do math. Not advanced math. Grade school math. The kind a 10-year-old solves"

The guess-the-next-words machines don’t actually understand anything.

https://nitter.poast.org/heynavtoor/status/2041243558833987600#m

#math #ai

Zundamon's Theorem is like THE BEST math YouTube channel. And by best I mean silly.

#math

📺 https://peer.adalta.social/w/mjzW4Y2EoQBG3rxJRM8U5h
🔗 [🇩🇪🇺🇸🇫🇷](https://adalta.info/articles/prstn_who_116330456243696530_fr)
🔗 [ℹ️](https://numbword.com/")

Une énigme mathématique parfaite, révélant des schémas de résolution complexes.

#game #puzzle #math #word #wordgames

📺 https://peer.adalta.social/w/6YAvi6rv1bkeHqpeDJTWRb
🔗 [🇩🇪🇺🇸🇫🇷](https://adalta.info/articles/prstn_who_116330456243696530_en)
🔗 [ℹ️](https://numbword.com/")

A Perfect Solution Reveals a Fundamental Flaw in the Game’s Design.

#game #puzzle #math #word #wordgames

📺 https://peer.adalta.social/w/58mBZLC7KXoTXd8eFNADs2
🔗 [🇩🇪🇺🇸🇫🇷](https://adalta.info/articles/prstn_who_116330456243696530_de)
🔗 [ℹ️](https://numbword.com/")

Die Lösung: Eine ungewöhnliche Zahlenfolge und ihre sprachliche Entsprechung.

#game #puzzle #math #word #wordgames

The futility of rushing too fast

Structurally it appear s very similar to the question off why buses often appear in threes’ and the stop go effect of red lights.

https://www.theguardian.com/technology/2026/apr/01/traffic-overtaking-slow-cars-catch-up-red-light-driving-research

#Traffic #Bunching #Mathematics #Math

Q: What numerical base do you use in your counting system?

A: 10

Geddit? Geddit?

#math #humor

Having sat with the notion for about six months now, I think Jay's critique of the Church-Turing thesis has legs. I don't see clearly yet exactly where and how the limits of computation manifest in his own system(s), which of course they must. But I think he's correct that this thesis as it's colloquially presented (and taught to students, including me!) is misleading at best and false in a certain important sense. Apparently he is regularly called a crackpot for forwarding this critique even though it's straightforwardly demonstrated.

Waaldijk's book is more of a constructive mathematics exploration. In this it is closely related to computer science, but it's focused on traditionally mathematical notions like topological space. The latter is usually quite complicated, but Waaldijk shows that the core concept of compact space can be represented with finitely-branching trees, making these spaces amenable to computation. Since we imagine physics taking place in spaces that are topological (among other things) there's potentially an interesting bidirectional flow of ideas between computer science and physics.

Jay calls his central notion "natural trees". Waaldijk calls his central notion "natural spaces". In both cases I think the intended sense is "with minimal artifice".

#ComputerScience #computation #math #mathematics #topology

One thing I like about this book is its approach to eigenvalues and eigenvectors. Most linear algebra books present eigenvalues as roots of the "characteristic polynomial", which is built from the "determinant", which in turn has some formula defining it. These objects are rarely motivated geometrically, and so you're left with limited understanding of just what an eigenvalue is or why linear transformations on finite-dimensional vector spaces must have them. Axler avoids determinants till Chapter 9 of the book, focusing instead on linear operators. The fact that operators must have eigenvalues pops out of the observation that iterating an operator on a given non-zero starting vector results in a set of vectors that must eventually become linearly dependent. This fact also leads to the development of the characteristic polynomial; you can then come at the determinant from this, more geometric, perspective.

#math #teaching #LinearAlgebra

#birthday #math #ComputerScience

#math #pens #chalk #Japan

I may go off about chalk someday, since I have strong opinions about it apparently.

#math #pen

Here's one. If you're given a function, you can treat argmax of that function as a set-valued function varying over all subsets of its domain, returning a subset--the argmaxima let's call them--of each subset. argmax x∈S f(x) is a subset of S, for any S that is a subset of the function f's domain. Another way to think of this is that argmax induces a 2-way partitioning of any such input set S into those elements that are in the argmax, and those that are not.

Now imagine you have some way of splitting any subset of some given set into two pieces, one piece containing the "preferred" elements and the other piece the rest, separating the chaff from the wheat if you will. It turns out that in a large variety of cases, given only a partitioning scheme like this, you can find a function for which the partitioning is argmax of that function. In fact you can say more: you can find a function whose codomain is (a subset of) some n-dimensional Euclidean space. You might have to relax the definition of argmax slightly (but not fatally) to make this work, but you frequently can (1). It's not obvious this should be true, because the partitioning scheme you started with could be anything at all (as long as it's deterministic--that bit's important). That's one thing that's interesting about this observation.

Another, deeper reason this is interesting (to me) is that it connects two concepts that superficially look different, one being "local" and the other "global". This notion of partitioning subsets into preferred/not preferred pieces is sometimes called a "solution concept"; the notion shows up in game theory, but is more general than that. You can think of it as a local way of identifying what's good: if you have a solution concept, then given a set of things, you're able to say which are good, regardless of the status of other things you can't see (because they're not in the set you're considering). On the other hand, the notion of argmax of a function is global in nature: the function is globally defined, over its entire domain, and the argmax of it tells you the (arg)maxima over the entire domain.

In evolutionary computation and artificial life, which is where I'm coming from, such a function is often called an "objective" (or "multiobjective") function, sometimes a "fitness" function. One of the provocative conclusions of what I've said above for these fields is that as soon as you have a deterministic way of discerning "good" from "bad" stuff--aka a solution concept--you automatically have globally-defined objectives. They might be unintelligible, difficult to find, or not very interesting or useful for whatever you're doing, but they are there nevertheless: the math says so. The reason this is provocative is that every few years in the evolutionary computation or artificial life literature there pops up some new variation of "fitnessless" or "objective-free" algorithms that claim to find good stuff of one sort of another without the need to define objective function(s), and/or without the need to explicitly climb them (2). The result I'm alluding to here strongly suggests that this way of thinking lacks a certain incisiveness: if your algorithm has a deterministic solution concept, and the algorithm is finding good stuff according to that solution concept, then it absolutely is ascending objectives. It's just that you've chosen to ignore them (3).

Anyway, returning to our friend argmax, it looks like it has a kind of inverse: given only the "behavior" of argmax of a function f over a set of subsets, you're often able to derive a function g that would lead to that same behavior. In general g will not be the same as f, but it will be a sibling of sorts. In other words there's an adjoint functor or something of that flavor hiding here! This is almost surely not a novel observation, but I can say that in all my years of math and computer science classes I never learned this. Maybe I slept through that lecture!

#ComputerScience #math #argmax #SolutionConcepts #CoevolutionaryAlgorithms #CooptimizationAlgorithms #optimization #EvolutionaryComputation #EvolutionaryAlgorithms #GeneticAlgorithms #ArtificialLife #InformativeDimensions

(2) The latest iteration of "open-endedness" has this quality; other variants include "novelty search" and "complexification".

(3) Which is fair of course--maybe these mystery objectives legitimately don't matter to whatever you're trying to accomplish. But in the interest of making progress at the level of ideas, I think it's important to be precise about one's commitments and premises, and to be aware of what constitutes an impossible premise.

There’s a fine line between a numerator and a denominator.

Only a fraction of people will find this funny.

#DadJokes #Puns #NotMyFault #Math

Say you have a notion of "context", and a way of ordering these so that some contexts are larger, more expansive than, or "above" others. And let's say in each context, there is a set of things that are identifiable as "best". I'm being vague because you can instantiate this basic idea pretty broadly. For instance, maybe the contexts are states of information in a search algorithm and "best" refers to the possible solutions that seem best in each state of information; as you search, you change (increase) your state of information, and might change your might about which possible solutions are the best one. As another example, the contexts could be possible worlds and "best" refers to which propositions are true in each possible world; as you progress from one possible world to the next, you might change your mind about what propositions are true.

Anyway, with that simple setup you can associate to each thing the set of all contexts in which it appears best. This set could be empty or could be very large or anything in between. Then the lower order shows up as a weak preference relationship among all the things: one thing is lower preference than another if, for each context in which it appears best, there's a larger or equal context in which the other thing seems best. Put differently, any time you think the first thing is best, there's a way to increase your context such that the other thing appears best. This is exactly the lower order between the sets of contexts in which each thing seems best. If the set of contexts in which one thing seems best is higher up the lower order (😝) than the set of contexts in which the other seems best, then the former thing is weakly preferred to the latter.

The intuition in a search setting is that contexts are states of information, a kind of compendium of what you've learned so far in your search. If x and y are possible solutions, and for every context (state of information) in which you think x is the best there is always a bigger context--i.e., with more information--in which you think y is best instead, you ought to prefer y to x. The rationale is that any time you think x is best there's a way to learn a little more and change your mind to think y is best instead, which justifies preferring y to x.

Applied to modal logic, this notion corresponds to validity: if in every possible world where the proposition p is true there is an accessible world in which proposition q is true, then "p implies possibly q" is true in every world (valid).

The appearance of "possibly" is suggestive I think, and concords with this being a weak preference. "Necessarily" would be a strong preference, but I'd expect (in the sense of demand) a search process follow such a preference directly.

#math #ComputerScience #search #CoevolutionaryAlgorithm #SolutionConcept #ModalLogic

#math #ComputerScience #OrderTheory

#SlowScience #math #CoevolutionaryAlgorithm #SolutionConcept

Alt...

Picture of a blackboard with some math scribbled on it. Below in the foreground there's a computer screen with some of the math typeset. I'm happy to describe to math to anyone who's interested but I'm not going to attempt to put a more detailed description here.

But the American Ornithological Society is making an effort with respect to bird names, and working through the controversies: https://americanornithology.org/english-bird-names/aos-pilot-project-to-change-harmful-english-common-bird-names/

and I think all of science and math can and should follow their lead. The world doesn't need "McCown's longspur" (McCown being a Confederate general complicit in genocide), and we don't need, for example, anything named after people like Gentzen either if you ask me: "In April 1939 Gentzen swore the oath of loyalty to Adolf Hitler as part of his academic appointment"; "Under a contract from the SS, Gentzen worked for the V-2 project" (from https://en.wikipedia.org/wiki/Gerhard_Gentzen)

#math #science #reform

Science results and math theorems should not be named after people, and we should undertake to rename any that currently are. We should prioritize renaming results or theorems named after white men and other privileged categories of people, with special attention to cases where a privileged person accepted or was assigned credit for work a less-privileged person did.

#math #science #reform